Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

<image>

The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

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In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

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Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in PYTHON3):

Solution:

def Check(Mat,Row,Col,TotalSum):
    N=len(Mat)
    M=len(Mat[0])
    SummTillNow=Row[0]*M+Col[0]*N
    for i in range(0,N):
        for j in range(0,M):
            if not (i==0 and j==0):
                if Mat[i][j]==0:
                    if (i in Row and Row[i]!=0) or (j in Col and Col[j]!=0):
                        return False
                    Row[i]=0
                    Col[j]=0
                elif i in Row and j in Col:
                    Val=Row[i]+Col[j]
                    if Val != Mat[i][j]:
                        return False
                elif i in Row:
                    Val=Mat[i][j]-Row[i]
                    if Val<0:
                        return False
                    Col[j]=Val
                    SummTillNow+=N*Val
                elif j in Col:
                    Val=Mat[i][j]-Col[j]
                    if Val<0:
                        return False
                    Row[i]=Val
                    SummTillNow+=M*Val
    if SummTillNow==TotalSum:
        return True
    return False


N,M=map(int,input().strip().split())
Mat=[]
for i in range(N):
    Mat.append(list(map(int,input().strip().split())))
Num=Mat[0][0]
TotalSum=0
Min_Count=float("inf")
for l in Mat:
    TotalSum+=sum(l)
for i in range(0,Num+1):
    Row={}
    Col={}
    Row[0]=i
    Col[0]=Num-i
    res=Check(Mat,Row,Col,TotalSum)
    if res:
        Count=0
        for k,v in Row.items():
            Count+=v
        for k,v in Col.items():
            Count+=v
        if Min_Count>Count:
            Min_Count=min(Min_Count,Count)
            AnsRow=Row
            AnsCol=Col
if Min_Count==float("inf"):
    print(-1)
else:
    print(Min_Count)
    for k,v in AnsRow.items():
        for cnt in range(v):
            print("row",k+1)
    for k,v in AnsCol.items():
        for cnt in range(v):
            print("col",k+1)